A loan of $10,000 is to be repaid by 60 monthly payments of $205.00 plus a smaller concluding payment made one month after the last $205 payment.Payments begin one month from now.If j₁₂ = 9%,find the amount of the smaller final payment.

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The loan repayment can be calculated using the formula for the present value of an annuity plus the present value of a single future payment. The total loan amount is the present value of 60 payments of $205 each, plus the present value of the final smaller payment. Using the given interest rate of 9% per annum, monthly interest rate is 0.75% (9% / 12 months). The present value of the annuity (60 payments of $205) can be calculated using the formula PV = PMT * [(1 - (1 + i)^-n) / i], where PMT is the payment amount, i is the monthly interest rate in decimal form, and n is the total number of payments. The present value of the final payment is calculated using the formula PV = FV / (1 + i)^n, where FV is the future value of the payment, i is the monthly interest rate in decimal form, and n is the number of periods until the payment is made. Subtracting the present value of the annuity from the total loan amount gives the present value of the final payment, which can then be adjusted to find its future value, or the amount of the final payment.

A Loan of $10,000 Is to Be Repaid by 60